The Obama-era Daca scheme was put in place to protect so-called “Dreamers”, migrants brought to the US illegally as children, from deportation.

The measures, which protect some 800,000 people in the US, also provide temporary permits for work and study.

Mr Trump announced on 4 September he would cancel the scheme, while giving Congress six months to enact a replacement plan for Daca recipients,

Following talks over dinner at the White House, House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer said: “We agreed to enshrine the protections of Daca into law quickly, and to work out a package of border security, excluding the wall, that’s acceptable to both sides.”

Democrats have repeatedly said that they will block any legislation that contains funding for the border wall – a key campaign pledge of Mr Trump’s.

A White House statement was more muted, simply saying that there had been a “constructive working dinner” where tax reform, border security and Daca had been discussed.

White House spokeswoman Sarah Sanders later disputed the Democrats’ account.

“While Daca and border security were both discussed, excluding the wall was certainly not agreed to,” she wrote on Twitter.

Mr Schumer’s aide replied: “The President made clear he would continue pushing the wall, just not as part of this agreement.”

Republican support would be needed in any immigration legislation, as they have a majority in both the House and the Senate.

Last week, Mr Trump stunned fellow Republicans by making a deal with the opposition Democrats to extend the US debt limit and extend the current budget to 8 December.